Use with Lesson
5-Minute Check
6-1
(over Chapter 5)
Solve.
4
1
1. Estimate. 3_
+ 2_
5
3
2
1
2. Subtract. 7_
- 4_
6
8
n
3. Solve. Check your solution. _
=7
3
4
7
4. Divide. 2_
÷_
5
20
3
-inch lengths can be cut from a
5. How many _
4
12-inch length of ribbon?
6.
Test Practice
Guy purchased a one-gallon
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
container of ether for a science experiment.
1
of the container was
When he was finished, _
16
full. How many fluid ounces of ether did Guy use?
A 8
B 12
C 64
D 120
ANSWERS
1. 6
5
2. 3_
24
3.
4.
5.
6.
21
8
16
D
Chapter 6
Glencoe Math Connects, Course 2
6–1
Ratios
GLE: NO:1B,1C
BUILD YOUR VOCABULARY (pages 121–122)
MAIN IDEA
• Write ratios as
fractions in simplest
form and determine
whether two ratios are
equivalent.
A
is a comparison of two quantities by division.
relationship between two
Ratios that express the
quantities are equivalent ratios.
EXAMPLE
Write Ratios in Simplest Form
APPLES Mr. Gale bought a basket
of apples. Using the table, write a
ratio comparing the Red Delicious
apples to the Granny Smith apples
as a fraction in simplest form.
Red Delicious
Granny Smith
Mr. Gale’s Apples
12 Fuji
9 Granny Smith
30 Red Delicious
10
30
30
_
=_
or
9
9
3
The ratio of Red Delicious apples to Granny Smith apples
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
is
EXAMPLE
.
Identify Equivalent Ratios
Determine whether the ratios 12 onions to 15 potatoes
and 32 onions to 40 potatoes are equivalent.
12 onions : 15 potatoes = __ or
12 ÷ 3
15 ÷ 3
®
ORGANIZE IT
Record a term or concept
from Lesson 6–1 under
the Ratios tab and write
a definition along with
an example to the right
of the definition.
32 onions : 40 potatoes =
32 ÷ 8
__
or
40 ÷ 8
The ratios simplify to the same fraction. They are
.
2ATIOS
2ATES
2ATEOF#HANGE
AND3LOPE
#USTOMARY -ETRIC5NITS
0ROPORTIONS
3CALE
IMALS
&RACTIONS$EC TS
AND0ERCEN
Math Connects, Course 2
123
6–1
Check Your Progress
a. FLOWERS A garden has 18 roses and 24 tulips. Write a
ratio comparing roses to tulips as a fraction in simplest form.
b. Determine whether the ratios 3 cups vinegar to 8 cups water
and 5 cups vinegar to 12 cups water are equivalent.
REMEMBER IT
Ratios such as
120 :1,800 can also be
written in simplest
form as 1:15.
EXAMPLE
POOLS It is recommended that no more than one person
be allowed into the shallow end of an outdoor public
pool for every 15 square feet of surface area. If a local
pool’s shallow end has a surface area of 1,800 square
feet, are the lifeguards correct to allow 120 people into
that part of the pool?
1:15 =
persons per square feet
Actual Ratio
120
120:1,800 = _
or
1,800
persons per square feet
Since the ratios simplify to the same fraction, they are
. The lifeguards are correct.
HOMEWORK
ASSIGNMENT
Page(s):
Check Your Progress SCHOOL A district claims that
they have 1 teacher for every 15 students. If they actually have
2,700 students and 135 teachers, is their claim correct?
Exercises:
124
Math Connects, Course 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Recommended Ratio
Score:________/________
10-Square Answer Sheet------MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
5-Minute Check
Use with Lesson
6-2
(over Lesson 6-1)
Write each ratio as a fraction in simplest form.
1. 36 to 21
2. 16 to 64
3. 22 meters to 180 meters
Determine whether the ratios are equivalent.
Explain.
4. 4:6 and 52:78
5. 8:17 and 32:64
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6.
Among the staff at Roosevelt
Elementary, 68 teachers prefer coffee and 20
prefer tea. Which ratio shows the relationship of
coffee drinkers to tea drinkers in simplest form?
Test Practice
A 10:34
B 17:5
C 5:17
D 34:10
ANSWERS
12
1. _
7
1
2. _
11
3. _
4
90
2
2
and 52:78 = _
4. Yes; 4:6 = _
3
3
8
8
1
1
, 32:64 = _
, and _
≠_
5. No; 8:17 = _
17
2
17
2
6. B
Chapter 6
Glencoe Math Connects, Course 2
6–2
Rates
GLE: AR:4A
BUILD YOUR VOCABULARY (pages 121–122)
MAIN IDEA
• Determine unit rates.
A ratio that
two quantities with different
kinds of units is called a rate.
When a rate is simplified so that it has a
of 1 unit, it is called a unit rate.
EXAMPLES
Find Unit Rates
®
ORGANIZE IT
Under the rate tab, take
notes on rate and unit
rate. Be sure to include
examples.
READING Julia read 52 pages in 2 hours. What is the
average number of pages she read per hour?
Write the rate as a fraction. Then find an equivalent rate with a
denominator of 1.
52 pages in 2 hours = __
2ATIOS
52 pages
2 hours
Write the rate as a
fraction.
52 pages ÷
Divide the
numerator and
denominator by
2ATES
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2ATEOF#HANGE
AND3LOPE
#USTOMARY -ETRIC5NITS
= ___
0ROPORTIONS
3CALE
2 hours ÷
IMALS
&RACTIONS$EC TS
AND0ERCEN
.
pages
= __
Simplify.
hours
SODA Find the unit price per can if it costs $3 for 6 cans
of soda. Round to the nearest hundredth if necessary.
$3 for 6 cans =
=
$3
__
6 cans
$3 ÷ 6
__
6 cans ÷ 6
= ___
Write the rate as a fraction.
Divide the numerator and the
denominator by 6.
Simplify.
Math Connects, Course 2
125
6–2
REMEMBER IT
The word rate is
often understood to
mean unit rate.
Check Your Progress Find each unit rate.
a. 16 laps in 4 minutes
EXAMPLE
b. $3 for one dozen cookies
Compare Using Unit Rates
TEST EXAMPLE The costs of 4 different sizes of orange
juice are shown in the table. Which container costs the
least per ounce?
Amount
Total Cost
16 oz
$1.28
32 oz
$1.92
64 oz
$2.56
96 oz
$3.36
A 96-oz container
C 32-oz container
B 64-oz container
D 16-oz container
Read the Item
Solve the Item
$1.28 ÷
ounces =
per ounce.
$1.92 ÷
ounces =
per ounce.
$2.56 ÷
ounces =
per ounce.
$3.36 ÷
ounces =
per ounce.
The
-ounce container of orange juice costs the least per
ounce. The answer is
126
Math Connects, Course 2
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find the unit price, or the cost per ounce of each size of orange
juice. Divide the price by the number of ounces.
6–2
Check Your Progress
MULTIPLE CHOICE The costs
of different sizes of bottles of
laundry detergent are shown
below. Which bottle costs the
least per ounce?
F 96-oz container
G 64-oz container
Amount
Total Cost
16 oz
$3.12
32 oz
$5.04
64 oz
$7.04
96 oz
$11.52
H 32-oz container
J 16-oz container
EXAMPLE
Use a Unit Rate
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
POTATOES An assistant cook peeled 18 potatoes in
6 minutes. At this rate, how many potatoes can he
peel in 50 minutes?
Find the unit rate.
18 potatoes in 6 minutes =
3 potatoes
__
· 50 min =
He can peel
HOMEWORK
ASSIGNMENT
6÷6
1
potatoes per minute.
The unit rate is
1 min
18 ÷ 6
3
__
=_
potatoes
potatoes in 50 minutes.
Check Your Progress Sarah can paint 21 beads in
7 minutes. At this rate, how many beads can she paint in
one hour?
Page(s):
Exercises:
Math Connects, Course 2
127
Score:________/________
20-Square Answer Sheet------MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
5-Minute Check
Use with Lesson
(over Lesson 6-2)
6-3
Find each unit rate. Round to the nearest
hundredth if necessary.
1. $3.99 for 16 ounces
2. 730 miles in 14 hours
3. $28 for 15 cassettes
4. Which is the better unit price: $1.99 for a 3-ounce
bottle or $2.49 for a 4-ounce bottle?
Determine whether the following statement is
sometimes, always, or never true. Explain by
giving an example or a counterexample.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. The denominator of a unit rate can be a decimal.
6.
Cassandra leaves college to go
home for the summer. She lives 424 miles away
and arrives in 8 hours. Which ratio shows her
rate of travel in simplest form?
Test Practice
A 53:1
B 53
C 1:53
D 212:4
ANSWERS
1. $0.25 per ounce
2. 52.14 miles per hour
3. $1.87 per cassette 4. $2.49 for a 4-ounce bottle
5. Never; A unit rate is a rate that is simplified so that
it has a denominator of 1 unit. For example, the
50 words
is read 50 words per minute.
unit rate _
1 minute
6. A
Chapter 6
Glencoe Math Connects, Course 2
6–3
A Plan for Problem Solving
GLE: AR:4A
MAIN IDEA
BUILD YOUR VOCABULARY (pages 121–122)
• Identify rate of change
A rate of change is a rate that describes how one quantity
changes in relation to another and is usually expressed as a
and slope using tables
and graphs.
.
EXAMPLE
Find Rate of Change from a Table
The table shows the number of miles a car drove on a
trip. Use the information to find the approximate rate of
change.
+ 65
Distance (miles)
Time (hours)
+ 65
+
65
130
195
260
1
2
3
4
+1
+1
The distance increased
change in time
miles for every hour.
So, the rate was 65 miles per hour.
WRITE IT
Check Your Progress The table shows the number of miles
a car drove on a trip. Use the information to find the rate of
change.
Explain how rate of
change is similar to unit
rates.
128
Math Connects, Course 2
Distance (miles)
Fuel (gallons)
44
88
132
176
2
4
6
8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
change in distance
____
=_
+1
6–3
BUILD YOUR VOCABULARY (pages 121–122)
The constant rate of change in y with respect to the
constant change in
EXAMPLE
ORGANIZE IT
Under the rate of
change and slope tab,
take notes on how to
find the slope of a line.
GRAPH THE DATA Find the slope of the line. Explain
what the slope represents.
Earnings
Graph the points and connect them
with a line.
Hours
Amount Earned
3
$45
6
$90
9
$135
2ATIOS
2ATES
2ATEOF#HANGE
AND3LOPE
#USTOMARY -ETRIC5NITS
0ROPORTIONS
3CALE
IMALS
&RACTIONS$EC TS
AND0ERCEN
Find Rate of Change from a Graph
Pick two points on the line, such
as (3, 45) and (6, 90), to find the
slope.
Amount Earned (dollars)
®
is called the slope of a line.
150
140 y
130
120
110
100
90
80
70
60
50
40
30
20
10
0
x
3
6
9
Hours
change in y
slope = __
change in x
90 -
___
6-
45
=_
or
3
The slope is
hour.
and represents the amount earned per
Check Your Progress The
table shows the cost of renting a
bicycle. Graph the data. Find the
slope of the line. Explain what
the slope represents.
Hours
Cost
2
$8
4
$16
6
$24
40
32
24
Cost ($)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
=
16
8
0
1
2
3
4
5
6
7
8
9
Hours
Math Connects, Course 2
129
Use with Lesson
5-Minute Check
6-4
(over Lesson 6-3)
1. The table shows the number of miles Greg walked
during a walk-a-thon. Use the information to find
the approximate rate of change in miles per hour.
Time (hr)
Distance (mi)
1
4
2
8
3
12
2. The graph represents the
number of patients that can
be seen in a doctor’s office
based on the number of
nurses on duty. Determine
the slope.
y
25
20
(4, 20)
15
(3, 15)
10
(2, 10)
5
(1, 5)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
0
3.
1
2
3
4
5
x
Use the information in the table to
find the rate of change.
Test Practice
Number of Students Number of Slices of Pizza
10
30
15
45
20
60
A 20 slices per student
C 3 students per slice
B 3 slices per student
D 20 students per pizza
ANSWERS
1. 4 miles per hour
2. 5 patients per nurse
3. B
Chapter 6
Glencoe Math Connects, Course 2
6–4
Measurement: Changing Customary Units
GLE: NO:2B,ME:1A
BUILD YOUR VOCABULARY (pages 121–122)
MAIN IDEA
A unit ratio is a ratio in which the denominator is
• Change units in the
unit.
customary system.
EXAMPLES
REMEMBER IT
You multiply to
change from larger
units of measure because
it takes more smaller
units than larger units to
measure an object.
Convert Larger Units to Smaller Units
Convert 2 miles into feet.
Since 1 mile = 5,280 feet, the unit ratio is
2 mi = 2 mi ·
5,280 ft
__
= 2 mi ·
5,280 ft
__
=
Multiply.
feet.
ELEVATOR The elevator in an office building has a
weight limit posted of one and a half tons. How many
pounds can the elevator safely hold?
1
1
t = 1_
t·
1_
2
2
Multiply by
since there are
pounds in 1 ton.
1
= 1_
· 2,000 lb or 3,000 lb
2
Multiply.
pounds.
So, the elevator can safely hold
Check Your Progress Complete.
a. 8 yd = ft
130
1 mi
Math Connects, Course 2
1
b. 4 _
T = lb
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Explain how estimating
can help you solve a
problem. (Lesson 6-1)
5,280 ft
__
.
Divide out common units.
1 mi
ft or 10,560 ft
So, 2 miles =
REVIEW IT
Multiply by
1 mi
.
6–4
EXAMPLES
Convert Smaller Units to Larger Units
Convert 11 cups into pints.
2c
, and its
Since 1 pint = 2 cups, the unit ratio is _
1 pt
reciprocal is
.
11 c = 11 c ·
1 pt
_
= 11 c ·
1 pt
_
Multiply by
2c
.
Divide out common units.
2c
= 11 ·
1
Multiplying 11 by _
is the same
11
=_
pt
2
2
as dividing 11 by 2.
=
pt
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
So, 11 cups =
pints.
SOCCER Tracy kicked a soccer ball 1,000 inches. How
many feet did she kick the ball?
Since 1 foot = 12 inches, multiply by
common units.
. Then divide out
1 ft
1,000 in. = 1,000 in. · _
12 in.
= 1,000 in. ·
1000
ft or
=_
12
ft
ft
So, Tracy kicked the soccer ball
.
Math Connects, Course 2
131
6–4
Check Your Progress Complete.
a. 21 qt = gal
b. 78 oz = lb
EXAMPLE
LEMONADE Paul made 6 pints of lemonade and poured it
into 10 glasses equally. How many cups of lemonade did
each glass contain?
Begin by converting 6 pints to cups.
6 pt = 6 pt ·
_
1 pt
= 6 · 2 cups or
cups
Find the unit rate which gives the number of cups per glass.
12 cups
6
__
=_
or
10 glasses
5
cups per glass
HOMEWORK
ASSIGNMENT
Page(s):
Exercises:
132
Math Connects, Course 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Check Your Progress CANDY Tom has 3 pounds of candy
he plans to divide evenly among himself and his 3 best friends.
How many ounces of candy will each of them get?
Score:________/________
30-Square Answer Sheet-----MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
5-Minute Check
Use with Lesson
(over Lesson 6-4)
6-5
Complete.
1. 21 ft =
yd
2. 160 oz =
lb
1
mi =
3. 1_
ft
4
4. 2 c =
fluid oz
5. Stella lives 2 miles from school. How many feet
from the school does Stella live?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6.
If 1,760 yards = 1 mile, then
4 miles = ___
__
? yards.
Test Practice
1
A_
4
B 4
C 440
D 7,040
ANSWERS
1. 7
2. 10
3. 6,600
4. 16
5. 10,560 feet
6. D
Chapter 6
Glencoe Math Connects, Course 2
6–5
Measurement: Changing Metric Units
GLE: NO:2B,ME:1A
BUILD YOUR VOCABULARY (pages 121–122)
MAIN IDEA
• Change metric units of
length, capacity, and
mass.
The metric system is a
system of measures.
The meter is the base unit of
.
The liter is the base unit of
The gram measures
.
.
The base unit of mass in the metric system is the
.
EXAMPLES
Convert Units in the Metric System
Complete 7.2 m = mm.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
To convert from meters to millimeters,
by
.
7.2 ×
=
So, 7.2 m =
mm.
®
ORGANIZE IT
Under the metric units
tab, take notes on
how to change metric
units, include examples
involving length,
capacity, and mass.
Complete 40 cm = m.
To convert from centimeters to meters,
40 ÷
So, 40 cm =
by
.
=
m.
2ATIOS
2ATES
2ATEOF#HANGE
AND3LOPE
#USTOMARY -ETRIC5NITS
0ROPORTIONS
3CALE
IMALS
&RACTIONS$EC TS
AND0ERCEN
Math Connects, Course 2
133
6–5
Check Your Progress Complete.
a. 7.5 m = cm
b. 3,400 mm = m
EXAMPLE
WRITE IT
Explain how you can
multiply a number by a
power of ten.
FARMS A bucket holds 12.8 liters of water. Find the
capacity of the bucket in milliliters.
to milliliters. Since the
You are converting from
bucket holds 12.8 liters, use the relationship 1 L =
1 L = 1,000 mL
mL.
Write the relationship.
× 1 L = 12.8 × 1,000 mL Multiply each side by 12.8
since you have 12.8 liters.
12.8 L =
mL
To multiply 12.8 by 1,000,
move the decimal point
places to the right.
mL.
Check Your Progress BOOKS A box of textbooks has
a mass of 32,850 grams. What is the mass of the box in
kilograms?
HOMEWORK
ASSIGNMENT
Page(s):
Exercises:
134
Math Connects, Course 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
So, the capacity of the bucket in milliliters is
Score:________/________
30-Square Answer Sheet-----MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
5-Minute Check
Use with Lesson
6-6
(over Lesson 6-5)
Complete.
1. 640 cm = 䊏 m
2. 0.05 m = 䊏 mm
3. 894 mg = 䊏 g
4. 124.5 kL = 䊏 L
5. 65,000 mL = 䊏 L
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6.
The longest suspension bridge in
the United States is the Verrazano-Narrows in
the Lower New York Bay. It spans 1,298 meters.
How many kilometers long is this bridge?
Test Practice
A 1,298,000 km
C 12.98 km
B 129.8 km
D 1.298 km
ANSWERS
1. 6.4
2. 50
3. 0.894
4. 124,500
5. 65
6. D
Chapter 6
Glencoe Math Connects, Course 2
6–6
6–1
Algebra: Solving Proportions
GLE: NO:3E
BUILD YOUR VOCABULARY (pages 121–122)
MAIN IDEA
Two quantities are proportional if they have a
• Solve proportions.
rate or ratio.
A proportion is an equation stating that two ratios or rates
.
are
In a proportion, a cross product is the
of
the numerator of one ratio and the denominator of the
other ratio.
KEY CONCEPT
Proportion A proportion
is an equation stating
that two ratios are
equivalent.
EXAMPLE
Identify Proportional Relationships
MATH Before dinner, Mohammed solved 8 math
problems in 12 minutes. After dinner, he solved
2 problems in 3 minutes. Is the number of problems
he solved proportional to the time?
.
compare ratios by comparing
problems
minutes
8
2
_
_
12
problems
minutes
3
8·3=
·2
24 = 24
Since the cross products are
, the number of
problems solved is proportional to the time.
136
Math Connects, Course 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
To identify proportional relationships, you can compare unit
rates or compare ratios by comparing cross products. Let’s
6–6
Check Your Progress Determine if the quantities $30
for 12 gallons of gasoline and $10 for 4 gallons of gasoline
are proportional.
EXAMPLES
Solve a Proportion
5
18
Solve _
=_
x .
8
18
_5 = _
Write the proportion.
x
8
5 · x = 8 · 18
5x =
Find the cross products.
Multiply.
5x
144
_
=_
Divide each side by
.
®
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
ORGANIZE IT
Under the proportions
tab, take notes on how
to solve a proportion.
Include examples.
x=
Simplify.
3.5
6
Solve _
=_
n.
14
3.5
6
_
=_
2ATIOS
14
2ATES
n
3.5 · n = 14 · 6
2ATEOF#HANGE
AND3LOPE
#USTOMARY -ETRIC5NITS
3.5n =
0ROPORTIONS
Write the proportion.
Find the cross products.
Multiply.
3CALE
84
3.5n
__
= __
IMALS
&RACTIONS$EC TS
AND0ERCEN
n=
HOMEWORK
ASSIGNMENT
Page(s):
Divide each side by
.
Simplify.
Check Your Progress Solve each proportion.
9
k
=_
a. _
15
18
4.6
_4
b. _
w =
5
Exercises:
Math Connects, Course 2
137
Score:________/________
15-Square Answer Sheet-----MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
5-Minute Check
Use with Lesson
(over Lesson 6-6)
6-7
Determine whether each pair of ratios forms
a proportion.
8
2
1. _
and _
12
1
2. _
and
9
3
and
3. _
4
48
3
_
36
4
_
5
Solve each proportion.
3
x
4. _
=_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7
21
6
18
=_
5. _
x
15
6.
The ratio of native Spanish
speakers to native English speakers in a local
high school is 3 to 8. If there are 254 students at
the school that are native English speakers, how
many students are native Spanish speakers?
Test Practice
A 32
ANSWERS
1. yes
2. no
3. no
Chapter 6
B 36
C 96
D 682
4. 9
5. 45
6. C
Glencoe Math Connects, Course 2
6–8
Scale Drawings
GLE: NO:3E, AR:3A, GR:3B
BUILD YOUR VOCABULARY (pages 121–122)
MAIN IDEA
Scale drawings and scale models are used to represent
• Solve problems
involving scale
drawings.
or too
objects that are too
to be
drawn at actual size.
The scale gives the ratio that compares the
of the drawing to the real object.
EXAMPLE
Use a Map Scale
MAPS What is the actual
distance between Portland
and Olympia?
®
,AKEWOOD
/LYMPIA
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
ORGANIZE IT
Under the scale tab,
explain how to solve a
problem involving scale
drawings. Be sure to
include an example.
Step 1 Use a ruler to find the
map distance between
the two cities. The
map distance is about
2ATIOS
2ATEOF#HANGE
AND3LOPE
#USTOMARY -ETRIC5NITS
0ROPORTIONS
3CALE
IMALS
&RACTIONS$EC TS
AND0ERCEN
6ANCOUVER
0ORTLAND
INCH
.
2ATES
-T3T(ELENgS
.ATIONAL
-ONUMENT
'RESHAM
MI
Step 2 Write and solve a proportion using the scale. Let
d represent the actual distance between the cities.
map
actual
_3
inch
1.69 inches
8
__
= __
map
_3 × d = 23 × 1.69
Cross products.
23 mi
d mi
8
actual
0.375d = 3.887
3
Multiply. Write _
8
as a decimal.
d=
Divide both sides
by 0.375.
The distance between the cities is about
kilometers.
Math Connects, Course 2
139
6–8
Check Your Progress MAPS On a map of California,
the distance between San Diego and Bakersfield is about
2
11 _
centimeters. What is the actual distance if the scale is
5
1 centimeter = 30 kilometers?
WRITE IT
Explain why these two
scales are equivalent
scales:
_1 inch = 4 miles
2
1 inch = 8 miles
EXAMPLE
Use a Blueprint Scale
ARCHITECTURE On the blueprint
of a new house, each square has
1
a side length of _
inch. If the length
4
SCALE
INÊÊ FT
of a bedroom on the blueprint is
1
inches, what is the actual length
1_
2
of the room?
Write and solve a proportion.
Scale
blueprint
Length of Room
t feet
actual
_1 · t =
15
_1 t = _
Multiply.
4
t=
The length of the room is
140
Math Connects, Course 2
actual
Cross products
4
4
blueprint
Simplify.
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
_1 inch
4
___ = ___
6–8
Check Your Progress On a blueprint of a new house,
1
each square has a side length of _
inch. If the width of the
4
kitchen on the blueprint is 2 inches, what is the actual width
of the room?
SCALE
INÊÊFT
EXAMPLE
Find a Scale Factor
Find the scale factor of a blueprint if the scale is
_1 inch = 3 feet.
2
_1
_1
inch
inch
2
2
__
= ___
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
_1
=
.
Convert 3 feet to
3 feet
inch
2
· __
Multiply by
to eliminate
36 inches
the fraction in the numerator.
=
Divide out the common units.
. That is, each measure on the
The scale factor is
blueprint is
HOMEWORK
ASSIGNMENT
the
measure.
Check Your Progress Find the scale factor of a blueprint if
the scale is 1 inch = 4 feet.
Page(s):
Exercises:
Math Connects, Course 2
141
Score:________/________
15-Square Answer Sheet-----MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
Use with Lesson
5-Minute Check
(over Lesson 6-8)
6-9
Suppose you are making a scale drawing. Find
the length of each object on the scale drawing
with the given scale. Then find the scale factor.
1. a subway car 34 feet long; 1 inch = 5 feet
2. a table 1.5 meters long; 3 centimeters = 0.25 meters
3. a football field that is 120 yards; 1 foot = 30 yards
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve.
4. The distance between New York City and
Washington, D.C., is 3.75 inches on a map of
the United States. If the scale on the map is
1 inch to 90 miles, how far is Washington, D.C.,
from New York City?
5.
Which ratio accurately shows the
relationship between the actual distance from
Atlanta to New Hope and the scale distance if the
actual distance is 425 miles and the scale
Test Practice
2
inches?
distance is 6_
3
2
A 6_
:425
3
3
B 1:63_
4
3
C 63_
:1
4
D 70.8:1
ANSWERS
4
1
1. 6_
in.; _
3
2. 18 cm; _
4. 337.5 mi
5. C
5
Chapter 6
60
25
1
3. 4 ft; _
90
Glencoe Math Connects, Course 2
Fractions, Decimals, and Percents
6–9
GLE: NO:1B
EXAMPLES
MAIN IDEA
• Write percents as
fractions and decimals
and vice versa.
Percents as Fractions
NUTRITION In a recent consumer poll, 41.8% of the
people surveyed said they gained nutrition knowledge
from family and friends. What fraction is this? Write in
simplest form.
Write a fraction with a
41.8
41.8% = _
100
denominator of 100.
41.8
=_
·
Multiply to eliminate the
decimal in the numerator.
100
=
or
Simplify.
1
Write 12 _
% as a fraction in simplest form.
2
_1
12
2
1
12 _
%=_
2
®
100
1
÷ 100
= 12 _
2
Write a fraction.
Divide.
=
÷ 100
1
Write 12 _
as an improper fraction.
=
×
Multiply by the reciprocal of 100.
2
Under the Fractions,
Decimals, and Percents
tab, take notes on
writing percents as
fractions and fractions
as percents. Include
examples.
=
or
Simplify.
Check Your Progress
2ATIOS
2ATES
2ATEOF#HANGE
AND3LOPE
#USTOMARY -ETRIC5NITS
0ROPORTIONS
a. ELECTION In a recent election, 64.8% of registered voters
actually voted. What fraction is this? Write in simplest form.
3CALE
IMALS
&RACTIONS$EC TS
AND0ERCEN
1
b. Write 62 _
% as a fraction in simplest form.
2
142
Math Connects, Course 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
ORGANIZE IT
6–9
KEY CONCEPTS
Common Fraction/
Decimal/Percent
Equivalents
_1 = 0.−3 = 33 _1 %
3
_2
3
_1
8
_3
8
_5
8
_7
8
=
=
=
=
=
3
−
_
0.6 = 66 2 %
3
1
0.125 = 12 _
%
2
1
0.375 = 37 _
%
2
1
0.625 = 62 _
%
2
1
0.875 = 87 _
%
2
EXAMPLES
Fractions as Percents
PRODUCE In one shipment of fruit to a grocery store,
5 out of 8 bananas were still green. Find this amount
as a percent.
n
_5 = _
8
100
500 = 8n
500
8n
_
=_
=n
5
1
So, _
= 62 _
% or
8
2
Write a proportion.
Find the cross products.
Divide each side by
.
Simplify.
.
5
Write _
as a percent. Round to the nearest hundredth
12
if necessary.
5
n
_
=_
12
Write a proportion.
100
=
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
500 12
Find the cross products.
ENTER
5
is about
So, _
12
41.66666667
Use a calculator.
.
3
Write _
as a percent. Round to the nearest hundredth.
7
3
_ = 0.4285714…
7
=
3
Write _
as a decimal.
7
by 100 and add the
.
Check Your Progress Write each fraction as a percent.
Round to the nearest hundredth.
13
a. _
HOMEWORK
ASSIGNMENT
Page(s):
Exercises:
25
11
b. _
15
Math Connects, Course 2
143
Score:________/________
40-Square Answer Sheet------MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________